Could you explain me please what does this question exactly want me to find? Or, how should I start solving ?
To solve this you need to:
It means that the sources have been connected for a long time and any transient response has died out.
So in this case you can use phasors to solve the problem.
When this circuit is put together (=connected the sources, before it zero voltage in the capacitors and zero current in the inductors) there starts some transient. One could easily see, how the currents and voltages fluctuate, but finally the transient dies and the currents and voltages stabilize to sinusoidal that have same frequency and constant amplitudes.
You must find those stabilized AC currents and voltages and their phase angles. The complex phasor calculus is the way to find the solution. Actually only one current is asked, so you can skip the others if your circuit analysis method does not need them as intermediate results.
With a mix of Cs and Ls, you may have numerous resonant frequencies.
All possible LC loops will store energy. That resonance may not show up, because of dampening or because of very low stimulus.